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Is Axler's Linear algebra done right insufficient for an introduction of the subject?

I have recognized the similar question, but I have a somewhat different situation. My familiarity with linear algebra is pretty much limited to basic matrix computation . I am currently in Multivariate Calculus and am looking for an introduction to linear algebra to prepare for future classes. The reason I mention Axler's is because it is the only book I have on hand, and I worry it is too abstract for an initial treatment. If any of you could clarify whether starting with this book is the right choice I would be delighted. Additionally, if you would recommend a different book for an introduction, what would you say?

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    $\begingroup$ Axler is intended as a second course in Linear Algebra, and my experience is that it works much better as a second course than a first one. $\endgroup$
    – Noah Snyder
    Commented Aug 29, 2020 at 21:52
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    $\begingroup$ Thank you! Are there any texts you would recommend for first course? Some texts I have pondered those by the authors of: Lay, Strang, Hoffman, Friedberg, Halmos. $\endgroup$
    – Groncow Bisnuts
    Commented Aug 29, 2020 at 21:55
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    $\begingroup$ I don't have a good sense of which of those would be best. I tried teaching an honors linear algebra class out of Axler and thought it was a mistake, but haven't had a chance to try a different book yet. $\endgroup$
    – Noah Snyder
    Commented Aug 29, 2020 at 22:07
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    $\begingroup$ I have no strong feelings on this, but wouldn't this question be better on MathStackExchange? $\endgroup$
    – paul garrett
    Commented Aug 29, 2020 at 22:07
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    $\begingroup$ As a first course for math/CS majors I prefer Lay who gives a good mix of theory and numerics. I hear that engineers like Strang. Personally, I find Strang handwavy and needlessly subtle/brief, especially in later chapters. Keep in mind that Strang writes for MIT students. $\endgroup$
    – Igor Belegradek
    Commented Aug 29, 2020 at 22:32

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(Pending moving this question to MathStackExchange, perhaps...)

Ironically, it may be best to learn/read "linear algebra done wrong" first, not only because it's what nearly everyone sees (so you'll have an idea what other people know/think), but because "doing it wrong" is in many ways very natural, even if considerably suboptimal in the long run. As with many mathematical things.

I myself have not kept up with introductory linear algebra texts, but, ... although years ago I was impatient with Strang's book because it was insufficiently modern/abstract, with some hindsight I tend to think that it is understandable by the students in the class... while my notion of "correct" linear algebra (notation, terminology, etc.) is not. The "right" version does not make sense until later, after having gone through the transitional stage of "doing things wrong".

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  • $\begingroup$ I appreciate your response greatly. I have lightly glossed over LADW in the past, and my only worry with it is, if it is viable as an introduction. Namely, does it provide suffient exercises and applications that are integral for understanding, or does it go straight into theory without computation. Pardon my potential naivety, as I am still not acquainted with the subject matter. $\endgroup$
    – Groncow Bisnuts
    Commented Aug 29, 2020 at 22:31
  • $\begingroup$ I don't have a copy of it to look at, and never really did look at its exercises and such... so, while I am confident that it aims to be pedagogically substantial, it may have some grudges or similar that skew the exercises. It is true that... with hindsight, as in many things... the exercises can be construed as reasonable, but my last impression from some years ago is that beginners would have trouble. Strang's book, the one I mainly remember, is much more accessible to beginners... even though in the long run I'd absolutely NOT take up that book's literal attitude about linear algebra. $\endgroup$
    – paul garrett
    Commented Aug 29, 2020 at 22:35

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